spring is zero. 2. A 100 g block is attached to a spring and undergoing simple h
ID: 1657371 • Letter: S
Question
spring is zero. 2. A 100 g block is attached to a spring and undergoing simple harmonic motion. Its position as a function of time ca be deibed by t)(10 cm) cos (10 rad/s t) a. What is the block's maximum speed and maximum acceleration? In Physics 221 we saw that we can often approach motion problems from different per spec tives and arrive at the same answer. For example, when dealing with masses on springs, we can think of things in terms of the relationship between kinematic quantities (position, velocity, acceleration) or in terms of energy b. Using the relationship between position and velocity, what is the position of the mass when it is moving at 60% of its maxinum speed? energy, what is the position of the mass when it is moving at 60% of its maximum spend?Explanation / Answer
a)x(t)=10cos(10t) cm
velocity = dx/dt = -100sin(10t) cm/s
acceleration = -1000cos(10t) cm/s2
Maximum speed is when sin(10t)=1 . maximum speed = 100cm/s = 1m/s
Maximum acceleration is when sin(10t)=1 . maximum acceleration = 1000 cm/s2 = 10m/s2
b) When it is moving at 60% of maximum speed,
60 = 100sin(10t)
sin(10t) = 0.6
cos(10t)=0.8
position at (cos10t)=0.8 is 10*0.8=8cm
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